The Converse Problem for the Multipotentialisation of Evolution Equations and Systems

DOI

10.1142/S1402925111001295How to use a DOI?

Keywords

Nonlinear evolution equations; potentialisation; auto-Bäcklund transformations; linearisation; the converse problem

Abstract

We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the converse problem. Although we mainly study a method for (1 + 1)-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-Bäcklund transformations for the equations/systems. In this respect we define the triangular-auto-Bäcklund transformation and derive its connections to the converse problem. Several explicit examples are given. In particular, we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.

Copyright

© 2011 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Norbert Euler
AU  - Marianna Euler
PY  - 2021
DA  - 2021/01/07
TI  - The Converse Problem for the Multipotentialisation of Evolution Equations and Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 77
EP  - 105
VL  - 18
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001295
DO  - 10.1142/S1402925111001295
ID  - Euler2021
ER  -